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Elodia [21]
3 years ago
5

Please help I’m confused because I this angle is less than 180 degrees but more than 90 degrees am I just totally wrong. I don’t

know I’m confused. Plz explain. Thx

Mathematics
1 answer:
zaharov [31]3 years ago
6 0

Answer:

  • "vertical" angles
  • x = 5
  • 35

Step-by-step explanation:

Angles on opposite sides of the point where lines cross are called "vertical angles." (The same lines define both angles, but they have only the vertex in common.) Their measure is irrelevant. The important characteristic of vertical angles is that they are equal in measure.

Since the angles have equal measures, we can equate the expressions for them:

  3x +20 = 10x -15

  35 = 7x . . . . . . . . . add 15-7x to both sides of the equation

  5 = x . . . . . . . . . . . divide by 7

Then the measure of the angles is ...

  3·5 +20 = 35

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Jon's coin collection consists of quarters, dimes and nickels. If the ratio of quarters to dimes is 5:2, and the ratio of dimes
Margarita [4]

Answer:

The ratio of quarters to nickels is:

  • <u>15:8</u>

Step-by-step explanation:

To solve the exercise, you must first consider how big is the ratio of each one to the other, when it is mentioned that the ratio of quarters to dimes is 5:2 it means that for every 5 quarters, Jon has 2 dimes, for the more quarters there are with respect to the dimes, we simply divide the larger value by the smaller:

  • 5/2 = 2.5

Thus, we know that there are 2.5 more quarters than dimes. Now the following proportion: the ratio of dimes to nickels is 3:4, which means that for every 3 dimes there are 4 nickels, as the nickels are greater in quantity, we are going to see how many times they are greater in proportion than the dimes making again a division of the major over the minor:

  • 4/3 = 1.33333333333 (<em>we are going to use the fractional number so as not to lose decimals</em>).

As we can see, the nickels are a little more than 1 with respect to the dimes, now we are going to create two formulas with those values:

  • <em>q = 2.5d </em>
  • <em>n = 4/3 d</em>

Where:

  • q = quarters
  • d = dimes
  • n = nickels

As you see. We only express the calculated proportions, at first glance you can identify that the number of quarters is greater, but to know how much greater with respect to nickels we are going to divide the two values ​​that accompany "d" in the formulas:

  • <u>2.5 / (4/3) = 15/8</u>

If we express it in ratio as it is in the exercise, we obtain:

  • <u>15:8</u>

So, <u>15:8 is the ratio of quarters to nickels</u>, <em>which means that for every 15 quarters, jon has 8 nickels.</em>

8 0
3 years ago
The area of the rectangle is 6 square feet. If its width is 2 1/7<br> ​feet, find its length.
densk [106]

Answer:

L = 2 4/5 feet

Step-by-step explanation:

A = L x W

6 = L x 2 1/7

divide both sides by 2 1/7

6 divided by 2 1/7 = L (is the same as multiplying by the reciprocal)

6 x 7/15 = L

L = 14/5 or 2 4/5

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What does 693 / 74 equal
lara31 [8.8K]
The answer is 9.37 when it is rounded up.
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Read 2 more answers
Length of the base of the given triangle is (x+3) units and the perpendicular height is (x-1)units. If the area of the triangle
Lana71 [14]

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

so, in our case we know this is 10 :

(x+3)(x-1)/2 = 10

(x+3)(x-1) = 20

x² - x + 3x - 3 = 20

x² + 2x - 23 = 0

that is exactly the provided equation. so, yes, x satisfies it.

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 2

c = -23

x = (-2 ± sqrt(2² - 4×1×-23))/(2×1) =

= (-2 ± sqrt(4 + 92))/2 = (-2 ± sqrt(96))/2 =

= (-2 ± sqrt(16×6))/2 = (-2 ± 4×sqrt(6))/2 =

= -1 ± 2×sqrt(6)

x1 = -1 + 2×sqrt(6) = 3.898979486... ≈ 4

or using sqrt(6) ≈ 2.45

= -1 + 2×2.45 = -1 + 4.9 = 3.9 ≈ 4

x2 = -1 - 2×sqrt(6) = -5.898979486... ≈ -6

or using sqrt(6) ≈ 2.45

= -1 - 2×2.45 = -1 - 4.9 = -5.9 ≈ -6

x2 would give us negative lengths for the triangle, which does not make sense.

so, x = 4 is our solution.

and that makes the height x-1 = 4-1 = 3 units.

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2 years ago
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